# Introduction to Variable Infiltration Capacity (VIC) Model

The first time I read about the VIC model, I thought it was very complicated and was glad that I didn’t have to deal with it. Today, almost a decade later (which is scary for a different reason), I can say that I’m happy that this model has been a big part of my research life. I (and a lot of wonderful people, including my Ph.D. advisor Dr. Jennifer Adam) spent a lot of time coupling VIC to a cropping system model. The result is called VIC-CropSyst. We have been using this coupled model to answer questions about how the water system and agricultural systems interact. More on this later.

In this blog post, I provide some theoretical background to the variable infiltration capacity model, also known as the VIC model. In a future post, I’ll provide some hands-on exercises, but the main purpose of the present post is to provide some general, high-level intuitions for first-time users. With a lot of caution, I’ll add, many of these descriptions are valid for some other hydrological and land-surface models.

First, VIC is a land-surface hydrological model (Hamman et al., 2018; Liang et al., 1994). What this means is that it simulates different components of water and energy balance over land-surface areas. These components include runoff generation, base flow generation, water movement in soil, evaporation, transpiration components, and cold-season processes.

VIC is a deterministic, process-based model, meaning that it uses theoretically or statistically derived relationships to simulate water- and energy-system components. Keep in mind that this doesn’t mean that all these underlying relationships are correct. Many of them have been developed in specific circumstances and might not hold in others, and many of them use simplifying assumptions to make complicated physical relationships usable. This could be an interesting topic for another post.

VIC is a large-scale model. It has been used for basin-wide, regional, continental and global simulation of hydrological processes. The grid-cell resolution is an arbitrary number, but I have seen simulations using resolutions from 1/16 of a degree to 2 degrees.

VIC also captures some key inter-grid cell variabilities. This means that when VIC simulates a grid cell, it divides the cells into subsections and simulates the hydrological processes for each of those. This is important because, as I mentioned, VIC is a large-scale model, and there might be a lot of variability within (let’s say) a 12 × 12 km grid cell. We might have lakes, mountains, valleys, forests, and agricultural land. VIC takes the original meteorological data and laps to different elevation levels of a grid cell (called snow bands in VIC).

VIC is also a spatially distributed model. This means that if you’re interested in running the model over a large basin, you need to divide the area into several grid cells with the same resolution. Then you run the model over each individual cell. The model’s time steps can range from hourly to daily.

In terms of time and space continuums, VIC has two main modes: (1) space before time, and (2) time before space. Each method comes with some computational pros and cons and some specific reasons. Space before time. In each time step, the model goes to one individual grid cell, runs for one time step, and then moves on to the next cell. When all the cells have been done for that time step, the model goes to the next time step and the process continues. Version 5 of VIC has the capability to simulate this, and this mode of the model is called image mode.

Time before space. The model starts the simulation with one grid cell, finishes it for all the time steps, and then moves on to the next cell. All versions of VIC can carry out time-before-space simulations .

Some More Technical Details

Variable infiltration capacity curve. As might be obvious from the name, this curve is one of the most important underlying processes in the model. A crucial part of each hydrological model is the partitioning of rainfall into runoff and infiltration. The basic idea came from a study of the spatial relations between runoff generation and soil moisture in large river basins (Xianjiang model; Zhao et al., 1980): when soil moisture is higher, more water goes into runoff, and when soil moisture is lower, infiltration is higher. The model uses these curves to partition precipitation into runoff and infiltration. The main parameter of the variable infiltration capacity curve (bi) is treated as a calibration parameter. Here is the VIC curve formula:

Movement of water in soil. VIC usually has three main soil layers. Once water enters the soil, it is distributed vertically from the top to the bottom layer. The top layer is usually 10 cm, which ensures that the calculation of evaporation from the soil is reasonable (see Liang et al., (1996)). The middle layer usually takes care of conveying the water to the next soil layer; it also acts as a reservoir of water for the crop root zone. The last layer is called the base flow layer. Once water reaches this layer, it stays there until it goes out of the system as base flow. The following figure shows a very simplified schematic of VIC soil layering system and sum of the key processes discussed here.

Base flow. VIC uses a two-stage base flow curve developed by Franchini and Pacciani, (1991). The first stage is linear. Basically, when the soil moisture is below a certain limit, the base flow generation has a linear relationship with soil moisture in the bottom layer of VIC (i.e., more moisture leads to more base flow). After that threshold, base flow generation increases exponentially with soil moisture until the soil moisture drops below that linearity limit. There are a few important calibration parameters in the formulation of base flow.

Energy balance. In each time step, VIC simulates many components of land-surface energy-related processes, such as snow accumulation and thawing, frozen soil and permafrost processes, evapotranspiration, and canopy-level energy budget (Cherkauer and Lettenmaier, 1999). Obviously, the different components of the energy balance are in continuous interaction with the water-balance components.

Model Inputs

At minimum, VIC needs the following information as inputs to the model: (1) meteorological data (e.g., minimum and maximum temperature, precipitation, and wind speed), (2) soil-texture information (e.g., hydraulic conductivity, initial moisture, moisture at field capacity, and permanent wilting point), and (3) land-use data (e.g., bare soil, open water, vegetation, depth of roots of the vegetation cover). However, the complete list of input parameters is much longer. I will go through these details in the next post.

Model Output

Some of the model’s fluxes and states are distributed by nature, such as evaporation, transpiration, and soil moisture. Others are aggregated, of which the most important is stream flow. To calculate stream flow, another step is needed to calculate runoff. VIC then aggregates the runoff and base flow generated from each individual grid cell to the outlet of basin. This process happens outside the main body of VIC (as a post-processing step) and is called routing (Lohmann et al., 1998). There are many other outputs users can choose at the end of simulation. For a complete list, look at this webpage.

To recap, the main focus of this is the VIC model. As I mentioned, however, VIC-CropSyst is a coupled version of VIC model, and in this version a process-based agricultural model is used to simulate agricultural processes such as crop growth, transpiration, root and shoot development, canopy coverage, and responses to climatic stressors. I haven’t covered it in this post, but maybe I’ll go back to it in a few months. In the meantime, for more information you can refer to (Malek et al., 2018, 2017).

References

Cherkauer, K.A., Lettenmaier, D.P., 1999. Hydrologic effects of frozen soils in the upper Mississippi River basin. J. Geophys. Res. Atmospheres 104, 19599–19610. https://doi.org/10.1029/1999JD900337

Franchini, M., Pacciani, M., 1991. Comparative analysis of several conceptual rainfall-runoff models. J. Hydrol. 122, 161–219. https://doi.org/10.1016/0022-1694(91)90178-K

Hamman, J.J. (ORCID:0000000174798439), Nijssen, B. (ORCID:0000000240620322), Bohn, T.J., Gergel, D.R., Mao, Y., 2018. The Variable Infiltration Capacity model version 5 (VIC-5): infrastructure improvements for new applications and reproducibility. Geosci. Model Dev. Online 11. https://doi.org/10.5194/gmd-11-3481-2018

Liang, X., Lettenmaier, D.P., Wood, E.F., Burges, S.J., 1994. A simple hydrologically based model of land surface water and energy fluxes for general circulation models. J. Geophys. Res. Atmospheres 99, 14415–14428. https://doi.org/10.1029/94JD00483

Liang, X., Wood, E.F., Lettenmaier, D.P., 1996. Surface soil moisture parameterization of the VIC-2L model: Evaluation and modification. Glob. Planet. Change 13, 195–206. https://doi.org/10.1016/0921-8181(95)00046-1

LOHMANN, D., RASCHKE, E., NIJSSEN, B., LETTENMAIER, D.P., 1998. Regional scale hydrology: I. Formulation of the VIC-2L model coupled to a routing model. Hydrol. Sci. J. 43, 131–141. https://doi.org/10.1080/02626669809492107

Malek, K., Adam, J.C., Stöckle, C.O., Peters, R.T., 2018. Climate change reduces water availability for agriculture by decreasing non-evaporative irrigation losses. J. Hydrol. 561, 444–460. https://doi.org/10.1016/j.jhydrol.2017.11.046

Malek, K., Stöckle, C., Chinnayakanahalli, K., Nelson, R., Liu, M., Rajagopalan, K., Barik, M., Adam, J.C., 2017. VIC–CropSyst-v2: A regional-scale modeling platform  to simulate the nexus of climate, hydrology, cropping  systems, and human decisions. Geosci Model Dev 10, 3059–3084. https://doi.org/10.5194/gmd-10-3059-2017

Zhao, R.J., Zhang, Y.L., Fang, L.R., others, 1980. The Xinanjiang model Hydrological Forecasting Proceedings Oxford Symposium. Oxford: IASH.